While silicon and gallium arsenide are dominant materials in modern micro- and nanoelectronics, devices fabricated
from them still use Si and GaAs substrates only separately. Integrating these materials on the large and cheep Si
substrate has been the subject of enormous research efforts for the past three decades. This review attempts to systematize
and generalize the current understanding of the fundamental physical mechanisms governing the epitaxial growth of GaAs
and related III-V compounds on Si substrates. Different kinds of bonding as a very promising non-epitaxial method for
III-V thin film integration on Si substrate are reviewed. Basic techniques available for improving the quality of such heterostructures
are described, and recent advances in fabricating of device-quality III-V-on-Si heterostructures and corresponding
devices are also presented.